Coverings, after the Prime Minister said a stricter approach was needed in england. Massacre, in which 8,000 Bosnian Muslim men and boys were murdered. Now on bbc news. This week marked the 80th anniversary of the start of the battle of britain, when the raf defended the country as nazi germany launched wave after wave of bombing raids over britain. The rafs young pilots held them off with their new fighter planes, the spitfires and hurricanes. The aircraft became iconic, a symbol of britains resilience under attack. But what has never been revealed before is the role that a schoolgirl from london played in their success, as Sophie Raworth has been finding out in the schoolgirl who helped winawar. Its a wonderful aircraft, absolutely wonderful. It fitted you like a glove, you see, thats what i liked about it. Without victory in the battle of britain, i think its almost certain that we would have been invaded by germany. It was a darn close run thing. It is the most famous plane from world war ii. It played a crucial role in the battle of britain. But what we didnt know until now was the role that a 13 Year Old Girl played in its design. Hazels role, like so many others, has hitherto been untold. I think we can look back and be extremely grateful for the contribution she made. Churchill we shall fight with growing confidence and growing strength in the air. We shall defend our island, whatever the cost may be. We shall never surrender. Newsreel way up in the sky, there are messerschmitts, junkers, heinkels and dorniers that are going to get the thrashing of their lives. In july 1940 the fate of the world hung in the balance. Britain was facing the threat of invasion from nazi germany. Adolf hitler knew that to win the war, he would need to invade britain. That summer, he made the decision to attack from the air, using the mighty german air force, the luftwaffe. The raf was outnumbered three to one. What followed in the skies above britain that summer has been described as this countrys single most important military campaign ever fought. Victory in the battle of britain was by no means certain, and depended on the skills and bravery of young raf pilots from britain and her allies. They were flying the latest generation of fighter planes, the legendary spitfires and hurricanes. A key feature of these fighters was the way they were armed. The new planes were initially designed to carry four machine guns, but in the run up to war, all that would change. Earlier this year i was lucky enough to find out what it was like to fly in one of these iconic planes. There we go. Its a low floor. Snug, isnt it . Amazing wow engine roars. Wow absolutely sensational. Being up here, the speed, the agility, the way the plane just. The pilot says youre almost flying it with your fingertips. Ijust cannot imagine being up here in a dogfight. Oh, my stomach wooh wow. I can feel the g force. Look at that. It is such an elegant and agile fighter. Speed and surprise were the key to its success. And, of course, its firepower. In we come to land. Pilots reckoned that they could keep their sights on for about two seconds. So you had to find a way of bringing down an enemy bomber in just two seconds. In 193a, as war with germany looked increasingly likely, the British Government took what many thought to be an extraordinary decision. The new generation of fighters, they said, should be armed with not four but eight browning machine guns. Newsreel give it up, mrs smith. Or is it miss . The battle of britain is your battle, too. Theys finally been persuaded by this man, a scientific officer in the air ministry called captain fred hill. He was convinced that withjust four guns, the planes being developed wouldnt have enough firepower to bring down fast moving enemy aircraft. He wanted to cram eight powerful machine guns onto the new fighter planes, an idea that seemed excessive to many. To bolster his case, fred turned to an unlikely person for help. A schoolgirl from north london his 13 year old daughter, hazel. Hazel was an only child, a talented mathematician and a meticulous worker. She had a close relationship with her father and was in many ways the ideal assistant for fred. Although just a teenager, it was hazel who helped complete the intricate calculations he had to make. Most people assumed that eight guns would be too heavy for the spitfire, that the extra load would make the nimble new aircraft slower and less manoeuvrable. Fred knew that a four gun design for the new fighters had already been agreed. If the plans were not changed quickly, it would be too late. So, its 1934. Youve got the hurricane and the spitfire under development. But its said that they only need four guns. You know they can catch the bombers, but now youve got to be able to kill them, and youve got three potential weapons available. One of them fires shells like this. This was a french hispano 20mm cannon, and its obviously very tempting to go for these. This one hits an airframe, its going to come down. Though there are problems with it. In order to be able to fire them accurately, theyve got to have a very stiff mounting, and as you can imagine, the weapon itself is very large. So its going to be difficult to find room in a spitfire wing, this very flexible wing, and even the hurricane, it turned out in practice, still didnt have a mounting stiff enough in order to be able to take any of these at the time. Your next choice would probably be this. This is actually a machine gun bullet, though it behaved more like a fast firing cannon, and its a. 5 inch machine gun. Now, those guns were still under development and they were very heavy. So, given the number that you would need to produce the density of fire required for that fire to be lethal against a contemporary bomber, youd need a lot of them. And so for the time being, at least, this option was laid on one side. What youre left with is this here. It looks a real tiddler, doesnt it . Its actually a. 303 rifle calibre machine gun bullet. Its the same thing that soldiers fired out of their rifles. However, it was discovered that if you grouped together eight of these machine guns, brownings firing a thousand rounds a minute, you would produce a density of fire of 256 rounds in the two seconds that it was assumed that a pilot would have in order to bring down a bomber. Two seconds was all he had, given the speed at which aircraft were moving now, and the difficulty of keeping your sights on. And these, eight of them, grouped together in the wings of hurricanes and spitfires, are what actually won the battle of britain. Without fred hills persistence, it could have been a very different outcome. He was so determined to prove the need for eight guns, not four, that he went home armed with the results of the most recent firing trials as well as one of the latest calculating machines. And he asked his daughter for help. Together, sitting around their small Kitchen Table in north london, they worked long into the night analysing the data. You wouldnt expect most 13 year olds to be able to do that kind of maths. So she must have been a pretty remarkable mathematician. A lot of this work was done clandestinely, in secret, by a few dedicated individuals who didnt really have any money available. But in a way, its not surprising. The budgets available to these people were very sparse, if indeed they had any budget at all. And in the accounts given by a lot of them, they talk about burning the midnight oil and coming into the office late after everybodys gone, to carry out further calculations and borrow some bits of equipment to carry out experiments, more or less off their own bat, where theyre working very long hours, because they were really dedicated to these things, and of course people taking their work home. This is raf duxford in cambridgeshire, home to many of the spitfires and hurricanes during the war. So this is a spitfire piece of history, almost . Absolutely, yes. And today, hazels sons have brought their mothers Kitchen Table here for us to see. So you have brought your Kitchen Table all the way from cornwall to here, the control tower at duxford. Explain why. I think its important for you to see it. This is the Kitchen Table at which my mother did the calculations for the guns on the aeroplanes that fought in the battle of britain, and i think if you are a 13 Year Old Girl, at your Kitchen Table, you can change the world. So theyve got the fabric over the gun ports, really nice and neatly. And before they went into action they used to just fire a couple of rounds to clear the fabric. Hazel told her sons about her role when they were growing up. And theyve long been fascinated by these planes. It was only after this work was presented that the change was made, and thats why my mother had to work so hard into the night, because there was only a small window of opportunity. The thing couldnt have gone into production if theyd spent months doing this, so it had to be done in weeks. What was it like for you as you unravelled the story . This cant be true . Its crazy. It seemed crazy that a 13 year old should be assisting the raf in working out how it should arm its fighters for the next war. You just think that this cant be right. The calculations hazel did on a machine like this were extremely complicated. I have to keep subtracting until the bell rings, then i move along. They showed that the future fighters needed to carry eight machine guns, each capable of firing at least 1000 rounds a minute, in order to have the firepower to destroy enemy planes. Captain fred hill presented this graph showing the analysis at the crucial meeting of the air ministry injuly 193a. But what only he and his superior officer knew was that the calculations that led to this conclusion had been done by his daughter, hazel. And eight guns at the time seemed an awful lot. They called it radical, didnt they . They called it staggering, and i think some of the higher echelons of the raf said, thats going a bit too far. Most of them had grown up with First World War fighters that had one or two guns on them. Four was radical eight was incredible. And in the end it was onlyjust enough to have the edge. Six years later, at the battle of britain, it was enough to win it, and if wed had less, if the calculations had not prove the point, it would have had a big impact. The only public recognition hazel had in her role of transferring the spitfires and hurricanes was in a memoir written by her fathers superior officer at the ministry until now, that is. Its wonderful that hazels story is at last reaching the light of day, and what a great inspiration for young people today, young girls in particular, that can look upon someone like hazel in the early 19305 making such an important contribution to our later success in the battle of britain, which was vital to this countrys survival. The calculations carried out by hazel and her father resulted in both spitfires and hurricanes being armed with eight rather than four guns. Over the next six years, as britain headed towards war with nazi germany, the planes were tested and put into production. Each gun carried just 300 rounds. It took around 15 seconds for them all to be fired. It meant that every bullet had to count. The spitfire was a nimble aircraft, perfect for dog fights,